求函数f(x)=(1/2) sin^2 x + cos ^2 x + (根号3 /4) sin2x 的最小正周期和值域

f(x)=(1/2) sin^2 x + cos ^2 x + (根号3 /4) sin2x
f(x)=(1/2)sin^2x+1/2cos^2x+1/2cos^2x+ (根号3 /4) sin2x
f(x)=1/4(1+cos2x)+1+ (根号3 /4) sin2x
f(x)=1/4cos2x+ (根号3 /4) sin2x +5/4
f(x)=根号[(1/4)^2+((根号3 /4) ^2]sin(2x+arctan(根号3/3))+5/4
f(x)=1/2sin(2x+pai/6)+5/4
T=2pia/2=pai
-1/2+5/4